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Simplifying 6x2 + -5x + -60 = 0 Reorder the terms: -60 + -5x + 6x2 = 0 Solving -60 + -5x + 6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -10 + -0.8333333333x + x2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + -0.8333333333x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + -0.8333333333x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -0.8333333333x + x2 = 0 + 10 -0.8333333333x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 -0.8333333333x + x2 = 10 The x term is -0.8333333333x. Take half its coefficient (-0.4166666667). Square it (0.1736111111) and add it to both sides. Add '0.1736111111' to each side of the equation. -0.8333333333x + 0.1736111111 + x2 = 10 + 0.1736111111 Reorder the terms: 0.1736111111 + -0.8333333333x + x2 = 10 + 0.1736111111 Combine like terms: 10 + 0.1736111111 = 10.1736111111 0.1736111111 + -0.8333333333x + x2 = 10.1736111111 Factor a perfect square on the left side: (x + -0.4166666667)(x + -0.4166666667) = 10.1736111111 Calculate the square root of the right side: 3.189609868 Break this problem into two subproblems by setting (x + -0.4166666667) equal to 3.189609868 and -3.189609868.Subproblem 1
x + -0.4166666667 = 3.189609868 Simplifying x + -0.4166666667 = 3.189609868 Reorder the terms: -0.4166666667 + x = 3.189609868 Solving -0.4166666667 + x = 3.189609868 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4166666667' to each side of the equation. -0.4166666667 + 0.4166666667 + x = 3.189609868 + 0.4166666667 Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000 0.0000000000 + x = 3.189609868 + 0.4166666667 x = 3.189609868 + 0.4166666667 Combine like terms: 3.189609868 + 0.4166666667 = 3.6062765347 x = 3.6062765347 Simplifying x = 3.6062765347Subproblem 2
x + -0.4166666667 = -3.189609868 Simplifying x + -0.4166666667 = -3.189609868 Reorder the terms: -0.4166666667 + x = -3.189609868 Solving -0.4166666667 + x = -3.189609868 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4166666667' to each side of the equation. -0.4166666667 + 0.4166666667 + x = -3.189609868 + 0.4166666667 Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000 0.0000000000 + x = -3.189609868 + 0.4166666667 x = -3.189609868 + 0.4166666667 Combine like terms: -3.189609868 + 0.4166666667 = -2.7729432013 x = -2.7729432013 Simplifying x = -2.7729432013Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.6062765347, -2.7729432013}
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